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Logic of if-then statement

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I am learning about Logic in an intermediate math class. I need some help with an if then statement.

So my sentence is...

If the Bible is the Word of God personally delivered by God to all of humanity, then...(fill in the blank)

We have been learning, The if...then statement is a common form of a logical statement. The only time the if...then statement is false is when the 'if' statement is true and the 'then' statement is false. For example, if you can earn an A in this class, then I will give you a million dollars. I don't have a million dollars so the 'then' statement is false. Now if you don't make an A in this class, then my if..then statement is true because the 'if' statement was not satisfied. If you do make an A in this class, then my if..then statement is false because the 'if' statement was satisfied but the 'then' statement was not.

Any help would be appreciated.

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Solution Preview

You clearly understand the logic of if-then statements. (Such a statement is also called an implication.)

If you want your if-then statement to be true, you need to be sure that if the "if" part of it is true then the "then" part of it is also true.

One possibility: If ...

Solution Summary

Some possible completions (possible wordings of the "then" part) of the given if-then statement are provided, along with a caveat as to the discernibility of whether they truly follow logically from the "if" part of that statement.

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Logic of the business process of using Structured English

In a relatively small company that sells thin, electronic keypads and switches, the rules for selling products are such that sales representatives are assigned to unique regions of the country. Sales come either from cold calling, referrals, or current customers with new orders. A sizable portion of their business comes from referrals from larger competitors who send their excess and/or "difficult" projects to this company. The company tracks these referrals and, similarly, returns the favors to these competitors by sending business their way.

The sales reps receive a 10 percent commission on actual purchases, not on orders, in their region. They can collaborate on a sale with reps in other regions and share the commissions, with 8 percent going to the "home" rep and 2 percent going to the "visiting" rep. For any sales beyond the rep's previously stated and approved individual annual sales goals, he or she receives an additional 5 percent commission, and additional end of the year bonus determined by management, and a special vacation for his or her family. Customers receive a 10 percent discount for any purchases over $100,000 per year, which are factored into the rep's commissions.

In addition, the company focuses on customer satisfaction with the product and service, so there is an annual survey of customers in which they rate the sales rep. These ratings are factored into the bonuses such that a high rating increases the bonus amount, a moderate rating does nothing, and a low rating can lower the bonus amount. The company also wants to ensure that the reps close all sales. Any differences between the amount of orders and actual purchases are also factored into the rep's bonus amount.

As best you can, present the logic of the business process first using Structured English, and then using a decision table. Write down any assumptions you have to make. Which technique is most helpful for this problem? Why?

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